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On the shortfall risk control: A refinement of the quantile hedging method

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  • Barski Michał

    (Mathematical Institute, University of Leipzig, Augustusplatz 10, 04109 Leipzig, Germany; and Faculty of Mathematics, Cardinal Stefan Wyszyński University in Warsaw, Wóycickiego 1/3, 01-938 Warsaw, Poland)

Abstract

The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minimizing setting is ruled out. The existence and concrete forms of optimal strategies in a general semimartingale market model with the use of conditional statistical tests are proven. The quantile hedging method applied in [Finance Stoch. 3 (1999), 251–273; Finance Stoch. 4 (2000), 117–146] as well as the classical Neyman–Pearson lemma are generalized. Optimal hedging strategies with shortfall constraints in the Black–Scholes and exponential Poisson model are explicitly determined.

Suggested Citation

  • Barski Michał, 2016. "On the shortfall risk control: A refinement of the quantile hedging method," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 125-141, March.
    • Handle: RePEc:bpj:strimo:v:32:y:2016:i:2:p:125-141:n:1
    DOI: 10.1515/strm-2014-1169
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    References listed on IDEAS

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